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\noindent The figure to the right provides an illustration of L’H\^o\-pi\-tal’s Rule.  Recall
that this rule can be applied when taking the limit as $x\longrightarrow x_a$
of a ratio of two functions where the ratio approaches the indeterminate form
$\frac{0}{0}$; in the case where both functions are differentiable at $x_a$,
the ratio approaches the ratio of their derivatives. In the case illustrated both
$\sin(x)$ and $x \longrightarrow0$ as we approach the origin, but the ratio of
their derivatives, $\frac{\cos(x)}{1} \longrightarrow 1$. L’H\^opital’s Rule
also applies in the case of the indeterminate form $\frac{\infty}{\infty}$.
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